SHEAR RUBBER

1.0 INTRODUCTION

Rubber is a unique material that is both elastic and viscous. Rubber parts can therefore function as shock and vibration isolators and/or as dampers. Although the term rubber is used rather loosely, it usually refers to the compounded and vulcanized material. In the raw state it is referred to as an elastomer. Vulcanization forms chemical bonds between adjacent elastomer chains and subsequently imparts dimensional stability, strength, and resilience.

Shear stress is a stress state where the stress is parallel to the surface of the material, as opposed to normal stress when the stress is vertical to the surface.

2.0 OBJECTIVE:

To measure the variation of deflection with applied load
Investigate relationship between shear stress and strain between rubber
To obtain Young modulus for rubber

3.0 THEORY

Shear stress: A form of stress that subjects an object to which force is appliedto skew, tending to cause shear strain.
Shear strain: The ratio of total deformation to the initial dimension of the material body in which the forces are being applied.

3.1 Shear stress

Shear stress can be defined as stress parallel to the plain and can be expressed as:

where ;

Shear stress can be illustrated as figure below:

Figure 3.1 Shear stress illustration on a square cube

3.2 Shear strain

Shear strain can defined as “deformation of a solid due to stress” and can be expressed as:

where

Figure 3.2 Shear strain illustration on square cube

3.4 Hooke’S law

Stress is proportional to the load and strain is proportional to the deformation as expressed with Hooke’s Law

where E is called as young modulus. Hooke’s law also can be written as

where G is called as shear modulus of rigidity.

4.0 PROCEDURE OF EXPERIMENT:

Firstly, the weight hanger is attached on the beam
The beam is put on the support
Adjust both parts on the beam using the screw on the supports, the tension spring and the screw on the top of the gauge
Zero the force gauge reading using the screw on the gauge
The load is put on the weight hanger and read the reading
The reading is recorded
Remove all the weight from the weight hanger. The weight hanger is put at different position and step 4 to 6 is repeated

Figure 4.1 : Equipment of the Experiment

4.1 Results

The dimension of rubber block:

Length, l : 0.073 m
Height, h: 0.152 m
Width, w: 0.025 m
Area, A: 0.0038 m^2

The area calculated is as follows Area = h*w = (0.152)(0.025) = 0.0038 m^2

Results from the experiment :

Table 4.1 : Result from experiment

Graph 4.1 : Graph of force against displacement

Graph 4.2 : Graph of Shear Stress(Pa) against Shear strain(rad)

5.0 Comsol Simulation

COMSOL multi physic is one of modelling software for finite element analysis. The applied load is same as experimental method which are 2, 4, 6 ,8, 10, 12, 14, 16, 18 and 20 N. Table 5.1 shows the displacement of the rubber obtained from COMSOL simulation. The graph of force against shear stress are plotted as in Figure 5.1. Complete simulation for each applied load are attached in attachment.

5.1 Procedure of Comsol

Space Dimension: 3-D
Physics:Solid Mechanics (Solid)
Study Type: Stationary
Geometry: width=0.025m , depth=0.073m, height=0.152m
Material Properties: E = 5.6 MPa, Poisson Ratio: 0.4

Boundary Condition: Total Force = -F at z-axis
Mesh Setting: Physics-controlled mesh, Extra Fine size
Parameter: F=[2,4,6,8,10,12,14,16,18 and 20]N
Plot Data: Displacement Field, y component

Results from COMSOL :

Table 6.1 : Result from COMSOL

Graph 5.1 Graph of Shear Force against Displacement for COMSOL

6.0 DISCUSSION

Graph 6.1 : Graph of Comparison between result obtained by Experiment and COMSOL

As can be seen in Graph 6.1, R-squared value obtained from COMSOL simulation is 1 while from experimental value is 0.9985. This shows that the analysis of shear rubber block from COMSOL simulation is assumed to be perfect and completely linear. The difference in displacement may be due to the error during the experiment. Besides that, the value of poison ratio of rubber used may not accurate.

7.0 Conclusion:

The graph of force against displacement above is plotted based on the data obtained from experiment and COMSOL software. The displacement obtained from experiment is higher compared to COMSOL.

8.0 Appendix:

2N 4N